On refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps
We present rational Lax representations for one-component parametric quadrirational Yang–Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang–Baxter maps (K-list), by considering the symmetries of the K-list ma...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000221 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We present rational Lax representations for one-component parametric quadrirational Yang–Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang–Baxter maps (K-list), by considering the symmetries of the K-list maps, we obtain compatible refactorization problems with rational Lax matrices for other classes of non-abelian involutive Yang–Baxter maps (Λ, H and F lists). In the abelian setting, this procedure generates rational Lax representations for the abelian Yang–Baxter maps of the F and H lists. Additionally, we provide examples of non-involutive (abelian and non-abelian) multi-parametric Yang–Baxter maps, along with their Lax representations, which lie outside the preceding lists. |
|---|---|
| ISSN: | 2666-8181 |